Oct. 14, 1996 to Oct. 16, 1996
F. Meyer auf der Heide , Dept. of Math. & Comput. Sci., Paderborn Univ., Germany
C. Scheideler , Dept. of Math. & Comput. Sci., Paderborn Univ., Germany
In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of size n, the routing number of H is defined as the maximum over all permutations /spl pi/ on [n] of the minimal number of steps to route /spl pi/ offline in H. We can show that for any network H of size n with routing number R our protocol needs O(log/sub R/ n/spl middot/R) time to route any permutation in H using only constant size edge buffers. This significantly improves all previously known results on deterministic routing. In particular our result yields optimal deterministic routing protocols for arbitrary networks with diameter /spl Omega/(n/sup /spl epsiv//) or bisection width O(n/sup 1-/spl epsiv//), /spl epsiv/>0 constant. Furthermore we can extend our result to deterministic compact routing. This yields, e.g., a deterministic routing protocol with runtime O((log n)/(log log n) R) for arbitrary bounded degree networks if only O(log n) bits are available at each node for storing routing information. Our proofs use a new protocol for routing arbitrary r/spl middot/s-relations in r-replicated s-ary Multibutterflies in optimal time O(log, n).
multiprocessor interconnection networks; deterministic routing; bounded buffers; online protocols; deterministic protocol; arbitrary permutations; arbitrary networks; r-replicated s-ary Multibutterflies
F. Meyer auf der Heide, C. Scheideler, "Deterministic routing with bounded buffers: turning offline into online protocols", FOCS, 1996, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 1996, pp. 370, doi:10.1109/SFCS.1996.548496